Calculate the Following Probabilities Using the Standard Normal Distribution $\operatorname { Pr } ( Z < 0.0 )$

question 42

Essay

Calculate the following probabilities using the standard normal distribution.Sketch the
probability distribution in each case, shading in the area of the calculated probability. (a) $\operatorname { Pr } ( Z < 0.0 )$
(b) $\operatorname { Pr } ( Z \leq 1.0 )$
(c) $\operatorname { Pr } ( Z > 1.96 )$
(d) $\operatorname { Pr } ( Z < - 2.0 )$
(e) $\operatorname { Pr } ( Z > 1.645 )$
(f) $\operatorname { Pr } ( Z > - 1.645 )$
(g) $\operatorname { Pr } ( - 1.96 < Z < 1.96 )$
(h) $\operatorname { Pr } ( Z < 2.576$ or $Z > 2.576 )$
(i) $\operatorname { Pr } ( Z > z ) = 0.10$ ; find $z$ .
(j) $\operatorname { Pr } ( Z < - z$ or $Z > z ) = 0.05$ ; find $z$ .

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Definitions:

Stocks and Bonds

Financial instruments that represent ownership in a company (stocks) and debt obligations (bonds), respectively, offering different levels of risk and potential returns.

Cash Flows

The aggregate sum of funds flowing in and out of a company, significantly influencing its ability to meet short-term obligations.

Expected Cash Flows

The anticipated stream of cash payments or receipts over a given period, used in evaluating investments or business projects.

Market

A venue or system where parties engage in exchange of goods, services, or information, including physical marketplaces or virtual markets.